Scheme for entanglement concentration of unknown W class states via linear optics

This paper proposes a scheme for entanglement concentration of unknown triparticle W class states with a certain probability. This protocol is mainly based on the coincidences of single-photon detectors and requires single-photon detectors and linear optical elements. The scheme is feasible within current technology.

Optimal entanglement concentration for three-photon W states with parity check measurement

We present an efficient entanglement concentration protocol（ECP） for the less-entangled W state with some identical conventional polarized single photons.In the protocol,two of the parties say Alice and Charlie should perform the parity check measurements and they can ultimately obtain the maximally entangled W state with a certain success probability.Otherwise,they can obtain another less-entangled W state,which can be reconcentrated into the maximally entangled W state.By iterating this ECP,a high success probability can be achieved.This ECP may be an optimal one and it is useful in current quantum information processing.

Efficient entanglement concentration for arbitrary less-entangled NOON state assisted by single photons

We put forward two efficient entanglement concentration protocols （ECPs） for arbitrary less-entangled NOON state. Both ECPs only require one pair of less-entangled NOON state and an auxiliary photon. In the first ECR the auxiliary photon is shared by two parties, while in the second ECP, the auxiliary photon is only possessed by one party, which can increase the practical success probability by avoiding the transmission loss and simplify the operations. Moreover, both ECPs can be used repeatedly to get a high success probability. Based on the above features, our two ECPs, especially the second one, may be useful in the quantum information processing.

Multipartite entanglement concentration of electron-spin states with CNOT gates

We propose a different entanglement concentration protocol （ECP） for nonlocal N-electron systems in a partially entangled Bell-type pure state using the CNOT gates and the projection measurements on an additional electron. For each nonlocal N-electron system, Alice first entangles it with the additional electron, and then she projects the additional electron onto an orthogonal basis for dividing the N-electron systems into two groups. In the first group, the N parties obtain a subset of N-electron systems in a maximally entangled state directly. In the second group, they obtain some less-entangled N-electron systems, which are the resource for the entanglement concentration in the next round. By iterating the entanglement concentration process several times, the present ECP has the maximal success probability, which is the theoretical limit of an ECP, equal to the entanglement of the partially entangled state, and higher than the others. This ECP may be useful in quantum computers based on electron-spin systems in the future.

Consequent entanglement concentration of a less-entangled electronic cluster state with controlled-not gates

We present a highly efficient entanglement concentration protocol （ECP） for a four-electron system in a less-entangled cluster state. In this ECP, we only require one pair of less-entangled electron cluster states and one ancillary electron to complete the task. With the help of the controlled-not （CNOT） gate, the concentrated maximally entangled state can be retained for further application with some success probability. On the other hand, the discarded items can be reused to obtain a high success probability. All the features make this ECP useful in the current quantum information field.

Efficient three-step entanglement concentration for an arbitrary four-photon cluster state

We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state.As a pioneering three-step entanglement concentration scheme,our protocol only needs a single-photon resource to assist the concentration in each step,which makes this protocol more economical.With the help of the linear optical elements and weak cross-Kerr nonlinearity,one can obtain a maximally-entangled cluster state via local operations and classical communication.Moreover,the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.

Entanglement concentration for an arbitrary hybrid less-entangled state and W state using quantum dots and a microcavity coupled system

We propose a practical entanglement concentration protocol （ECP） for a hybrid entangled state using quantum dots and a microcavity coupled system. A hybrid less-entangled state can he concentrated to a most-entangled state with a certain probability using only one ancillary single photon. Moreover, using this protocol, we can also concentrate an arbitrary three-particle less-entangled W state using two ancillary photons and classical communication. The proposed protocols provide us with a useful method to concentrate less-entangled states, which can he implemented with current technology.

Electronic cluster state entanglement concentration based on charge detection

We propose an efficient entanglement concentration protocol （ECP） based on electron-spin cluster states assisted with single electrons. In the ECP, we adopt the electron polarization beam splitter （PBS） and the charge detector to construct the quantum nondemolition measurement. According to the result of the measurement of the charge detection, we can ultimately obtain the maximally entangled cluster states. Moreover, the discarded items can be reused in the next round to reach a high success probability. This ECP may be useful in current solid quantum computation.

Efficient electronic entanglement concentration assisted by single mobile electrons

We present an efficient entanglement concentration protocol （ECP） for mobile electrons with charge detection. This protocol is quite different from other ECPs for one can obtain a maximally entangled pair from a pair of less-entangled state and a single mobile electron with a certain probability. With the help of charge detection, it can be repeated to reach a higher success probability. It also does not need to know the coefficient of the original less-entangled states. All these advantages may make this protocol useful in current distributed quantum information processing.

Entanglement concentration for W-type entangled coherent states

An entangled coherent state （ECS） is one type of entanglement, which is widely discussed in the application of quan- tum information processing （QIP）. In this paper, we propose an entanglement concentration protocol （ECP） to distill the maximally entangled W-type ECS from the partially entangled W-type ECS. In the ECP, we adopt the balanced beam split- ter （BS） to make the parity check measurement. Our ECP is quite different from the conventional ECPs. After performing the ECP, not only can we obtain the maximally entangled ECS with some success probability, but also we can increase the amplitude of the coherent state. Therefore, it is especially useful in long-distance quantum communication, if the photon loss is considered.

Scheme for Entanglement Concentration of Unknown Multiparticle Greenberger-Horne-Zeilinger or W Class States

We present,two schemes for concentrating unknown nonmaximally entangled Greenberger Horme-Zeilinger(GHZ) or W class states.The first scheme for concentrating the nonmaximally entangled GHZ state is based on linearoptical devices.The second scheme for concentrating the W class states can be applied to a wide variety of atomic state.Both of our schemes are not postselection ones and are within the current technologies.

Hybrid entanglement concentration assisted with single coherent state

Hybrid entangled state （HES） is a new type of entanglement, which combines the advantages of an entangled po- larization state and an entangled coherent state. HES is widely discussed in the applications of quantum communication and computation. In this paper, we propose three entanglement concentration protocols （ECPs） for Bell-type HES, W-type HES, and cluster-type HES, respectively. After performing these ECPs, we can obtain the maximally entangled HES with some success probability. All the ECPs exploit the single coherent state to complete the concentration. These protocols are based on the linear optics, which are feasible in future experiments.

Optimal multi-photon entanglement concentration with the photonic Faraday rotation

We put forward an optimal entanglement concentration protocol（ECP） for recovering an arbitrary less-entangled multi-photon Greenberger–Horne–Zeilinger（GHZ） state into the maximally entangled GHZ state based on the photonic Faraday rotation in low-quality（Q） cavity. In the ECP, only one pair of less-entangled multi-photon GHZ state and one auxiliary photon are required, and the concentration task can be realized by local operations. Moreover, our ECP can be used repeatedly to further concentrate the discarded items of conventional ECPs, which can increase its success probability largely. Under the practical imperfect detection condition, our protocol can still work with relatively high success probability. This ECP has application potential in current and future quantum communication.

Heralded entanglement concentration for photon systems with linear-optical elements

We present two nonlocal entanglement concentration protocols(ECPs)to distill a subset of N-photon systems in a GreenbergerHorne-Zeilinger(GHZ)state or a W state from a set of photon systems in a partially entangled GHZ-like pure state or a lessentangled W-like state with known parameters,respectively.Our ECPs have some advantages.First,our ECPs work in a heralded way with linear-optical elements only,without the postselection based on nonlinear optics,far different from the previous ECPs.Second,they require only a copy of the less-entangled photon system in each round of the entanglement concentration process,not two copies,which decreases the difficulty of their implementation in experiment largely.Third,our ECPs avoid checking the photon number in the output modes of linear-optical elements with the sophisticated single-photon detectors.Moreover,all parties can operate the process for concentration simultaneously and independently,which leads to flexible operations and improves the performance greatly in experiment.These advantages make our ECPs useful in practical applications in long-distance quantum communication network.

Entanglement concentration with strong projective measurement in an optomechanical system

In this work, we study an entanglement concentration scheme in a 3-mode optomechanical system. The scheme is based on phonon counting measurements, which can be performed through photon counting of an auxiliary cavity connected to the mechanical resonator. The amount of entanglement between the two cavity output modes is found to increase logarithmically with the number of detected phonons(photons). Such an entanglement concentration scheme is deterministic since, independently of the number of detected phonons(photons), the measurement always leads to an increase in output entanglement. Besides numerical simulations,we provide analytical results and physical insight for the improved entanglement and the concentration efficiency.

Entanglement concentration for a non-maximally entangled four-photon cluster state

We present a scheme for locally concentrating a non-maximally entangled four-photon cluster state into a maximally-entangled four-photon cluster state. This scheme has a high success probability. The controlled-NOT （CNOT） gate is a crucial ingredient in this scheme, and we use a nearly deterministic CNOT gate, which is similar with that first introduced by Nemoto et al. （Phgs. Rev. Lett., 2004, 93： 250502）. This CNOT gate has a simple structure and does not need the strong nonlinearity.

Efficient nonlocal two-step entanglement concentration protocol for three-level atoms in an arbitrary less-entangled W state using cavity input-output process

We present an efficient two-step entanglement concentration protocol(ECP)for three-level atoms trapped in one-sided optical micro-cavities in an arbitrary three-particle less-entangled W state,using the coherent state input-output process in low-Q cavity quantum electrodynamics system.In each step of the new proposed protocol,one of the three remote users prepares the auxiliary coherent optical pulses to perform cavity input-output process and then utilizes the standard homodyne measurement to discriminate the final outgoing coherent states.When both of the two steps are successful,remote parties can deterministically concentrate the less-entangled W state atoms to a standard maximally entangled W state.Compared with previous ECPs for W state,this protocol has some advantages and can be widely used in current quantum repeater and some quantum information processing tasks.

On Extension of Optimal Entanglement Concentration of GHZ States in Quantum-Dot and Micro-Cavity Coupled System

We extend an optimal entanglement distillation of the triplet Greenberger–Horne–Zeilinger(GHZ) state via entanglement concentrating in the three-partite partially electron-spin-entangled systems. Two entanglement concentration protocols are similarly designed in detail with the post-selection in quantum-dot(QD) and micro-cavity coupled systems. The proposed protocol can be repeated several rounds to achieve an optimal success probability with an assistance of the ancillary QD, where only the single photon needs to pass through the micro-cavity for each round. It increases the total success probability of the distillation even if the implemented cavity is imperfect in practice during the whole process.

Entanglement Concentration with Different Measurement in a 3-Mode Optomechanical System

In this work, we perform a series of phonon counting measurement with different methods in a 3-mode optomechanical system, and we compare the difference of the entanglement after measurement. In this article we focus on the three eases： prefect measurement, imperfect measurement and on-off measurement. We find that whatever measurement you take, the entanglement will increase. The size of entanglement enhancement is the largest in the perfect measurement, second in the imperfect measurement, and it is not obvious in the on-off measurement. We are sure that the more precise measurement information, the larger entanglement concentration.

Concentration Scheme for Partially Entangled Atomic States Through Detection of Cavity Decay

We propose a scheme for concentrating entanglement of partially entangled states for atoms trapped in the distant cavities. The scheme is based on adiabatic passage and photonic interference. It is robust against a number of practical noises such as the violation of the Lamb-Dicke condition, spontaneous emission and detection inefficiency.